Abstract: We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (herding) and the aspiration of sticking with the own type (stubbornness). While the corresponding N-player game possesses a unique Nash equilibrium, the mean field game has a variety of equilibria and phase transitions. The large N limit of the unique equilibrium of the N-player game selects one equilibrium of the mean field game; this selection appears to be highly nontrivial and will be discussed mostly on the base of simulations.